1962-1964年におけるわが国地域間物資輸送構造の解析

抄録

We can make a varietal model of the quantity of the goods transported from the ith region to the jth region written by the equation: being based on the Isard's gravity model¹⁾ which is originally constructed for the number of trips and is expressed by the equation: where Wi., W.j and W.. are _??_ Wij, _??_ Wij, and _??_ Wij respectively (n is the total number of regions) Dij is the distance from the ith region to the jth region, k and α are parameters, and Kij and αij are the particular parameters for Wij.
If we multiply the right hand side of the equation (1) by the values Pi/Pi, Pj/Pj, and P/P and we assume the values Wi/Pi, W.j/Pj, and W../P are th_??_ functions of yi, yj, and y, we can obtain the following model: where Pi and Pj are the populations of the ith and jth region, P is the population of all the regions observed, yi and yj are the per capita output of the ith and jth region and y is the per capita output of all the regions observed.
On the other hand, the relation expressed by the equations: are found from some of the data of Japan for the years 1962-1964.²⁾ Being based upon the relations, the model shown by the equation (5) is constructed. whereKij is kij ki. k.j/k... In this model, Wij is explained by regional economic activities and populations, and the distance between regions.
When we have sufficient data of time series, we can get the values of the parameters in the equation (5) by the method of least squares, using the form: But, unfortunately, the values of the parameters can not be found from the data of Japan for the years 1962-1964, because the size of the data is so small that we can not calculate the values of the parameters.
However, if we assume that the values of the parameters Kij, βi., β.j, and αij are K, β, β′, and α for each i and j respectively, we can get the following model: where β″ is β.. . And we would be able to get the values of the parameters of the model by the data for the 3 years, because from the OD tables for the 3 years we can obtain many actual values of Wij.
Really, the model was tentatively applied to the data of Japan for the years 1962-1964. But, the model was not successfully applied to the data. The model shown by the equation (1) was successfully applied to the data.
Incidentally, W. Leontief and A. Strout³⁾ have tried to extract the effects of the ith and the jth region on the Wij by two kinds of parameters. If the model expressed by the equation (6) is successfully applied to the data, we would be able to extract the effects of the ith and the jth region by the parameters βi. and β.j, and the particular characters of the connection between the ith and the jth region by the parameters Kij and αij.